(Biran-)Nagata conjecture for multipoint Seshadri constants

Let $X$ be a surface and let $H\in\operatorname{Pic} X$ be an ample divisor. For a positive integer $r$, write $\varepsilon(H,r)$ for the multipoint Seshadri constant at $r$ points. (Biran-)Nagata conjecture.

$$\varepsilon(H,r)=\sqrt{\frac{H.H}{r}}$$

for all sufficiently large $r$. This is the long-standing Nagata conjecture, here linked to the geometry of nested Hilbert schemes; the supplied context does not state whether it has been resolved in this generality.